Least Common Multiple (LCM) of 34 and 200
The least common multiple (LCM) of 34 and 200 is 3400.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 34 and 200?
First, calculate the GCD of 34 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 200 = 0 remainder 34 |
| 2 | 200 ÷ 34 = 5 remainder 30 |
| 3 | 34 ÷ 30 = 1 remainder 4 |
| 4 | 30 ÷ 4 = 7 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 47 | 1504 |
| 13 and 10 | 130 |
| 23 and 91 | 2093 |
| 17 and 113 | 1921 |
| 105 and 155 | 3255 |